Second-order time integrators with the Fourier spectral method in application to multidimensional space-fractional FitzHugh-Nagumo model

Harish Bhatt; Harish Bhatt

doi:10.3934/era.2023369

Electronic Research Archive

2023, Volume 31, Issue 12: 7284-7306. doi: 10.3934/era.2023369

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Second-order time integrators with the Fourier spectral method in application to multidimensional space-fractional FitzHugh-Nagumo model

Harish Bhatt ^,

Department of Mathematics, Utah Valley University, UT 84058, USA

Received: 29 August 2023 Revised: 19 October 2023 Accepted: 02 November 2023 Published: 14 November 2023

This paper investigated the propagation and interaction behavior of the fractional-in-space multidimensional FitzHugh-Nagumo model using second-order time integrators in combination with the Fourier spectral method. The study focused on analyzing the accuracy, efficiency and stability of these time integrators by comparing numerical results. The experimental findings highlight the ease of implementation and suitability of the methods for long-time simulations. Furthermore, the method's capability to capture the influence of the fractional operator on the equation's dynamics was examined.
- fourier spectral method,
- second-order time integrators,
- space-fractional reaction-diffusion systems,
- excitable systems,
- FitzHugh-Nagumo model
Citation: Harish Bhatt. Second-order time integrators with the Fourier spectral method in application to multidimensional space-fractional FitzHugh-Nagumo model[J]. Electronic Research Archive, 2023, 31(12): 7284-7306. doi: 10.3934/era.2023369

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Abstract

This paper investigated the propagation and interaction behavior of the fractional-in-space multidimensional FitzHugh-Nagumo model using second-order time integrators in combination with the Fourier spectral method. The study focused on analyzing the accuracy, efficiency and stability of these time integrators by comparing numerical results. The experimental findings highlight the ease of implementation and suitability of the methods for long-time simulations. Furthermore, the method's capability to capture the influence of the fractional operator on the equation's dynamics was examined.

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